Function Of System Parameters Research Articles

Dynamical system model of gentrification: Exploring a simple rent control strategy.

Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the nonrent control model; in fact, long-lived transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.

Motion behaviors of droplets containing Au nanoparticles on a superhydrophobic laser-induced graphene surface

The movement of nanoparticle-containing droplets on solid surfaces significantly affects the distribution of the nanoparticles and is of great interest in the fields of two-phase separation, biosensing detection, inkjet printing, and microarrays. There has been little research on the initiation and motion behaviors of colloidal droplets containing nanoparticles on superhydrophobic surfaces. Here, we prepare superhydrophobic laser-induced graphene (LIG) surfaces with excellent depinning effects using an extremely simple method and explore the formation mechanism of the depinning-LIG surfaces. The reduction of nano-graphene fibers and the increased hydroxyl group ratio after alcohol modification further enhance the hydrophobic properties of depinning-LIG, reducing its surface adhesion. The initial and continuous motion of droplets containing Au nanoparticles (AuNPs) on these superhydrophobic surfaces under airflow is studied using high-speed microscopy. The coupling effects of the droplet size, surface properties, airflow velocity, and nanoparticles on the droplet motion behaviors are analyzed. The dimensionless parameter G is incorporated to obtain the partition diagram of AuNP droplet motion behaviors on depinning-LIG surfaces, which delineate the critical conditions for droplet “oscillation,” “initiate sliding,” and “continuous rolling” as a function of system parameters. For AuNP droplets, the viscous force Fγ,p exerted by the nanoparticles on the contact line significantly affects the droplet movement behaviors. In addition, a mathematical model about the competition of dynamic forces and resistance is established to describe the motion of AuNP droplets, and the critical conditions for different motion behaviors of the droplet are clarified to guide practical applications.

Threshold-impeded stochastic production: how noise interacts with disruptive thresholds to affect the production output in fluctuating environments

Introduction: Production systems are bound to operate in stochastic conditions. Prominent sources of performance-reducing uncertainty are constituted by machine failures, decision errors, and fluctuating supplies. This article offers a novel approach to uncertainty through modelling and simulation of nonlinear production systems. In particular, the authors consider production systems where the output is drastically reduced when a resource of fluctuating input values reaches an upper threshold.Methods: The article introduces minimal models of such hreshold-impeded stochastic production (TISP) systems and the system performance (i.e., the output) is analyzed as a function of system parameters (e.g., the type of nonlinearity) and noise input features (e.g., the distribution width or time correlations). Applications to steel manufacturing via continuous casting and power generation through wind turbines are discussed in detail.Results and Discussion: The simulation experiments illustrate that especially the extent of the input fluctuations affects the output performance which is why the authors recommend that TISP system operators counterbalance such fluctuations if possible.

Liquid-Liquid Dispersion Performance Prediction and Uncertainty Quantification Using Recurrent Neural Networks.

We demonstrate the application of a recurrent neural network (RNN) to perform multistep and multivariate time-series performance predictions for stirred and static mixers as exemplars of complex multiphase systems. We employ two network architectures in this study, fitted with either long short-term memory and gated recurrent unit cells, which are trained on high-fidelity, three-dimensional, computational fluid dynamics simulations of the mixer performance, in the presence and absence of surfactants, in terms of drop size distributions and interfacial areas as a function of system parameters; these include physicochemical properties, mixer geometry, and operating conditions. Our results demonstrate that while it is possible to train RNNs with a single fully connected layer more efficiently than with an encoder-decoder structure, the latter is shown to be more capable of learning long-term dynamics underlying dispersion metrics. Details of the methodology are presented, which include data preprocessing, RNN model exploration, and methods for model performance visualization; an ensemble-based procedure is also introduced to provide a measure of the model uncertainty. The workflow is designed to be generic and can be deployed to make predictions in other industrial applications with similar time-series data.

Proportional Fairness for Long-Term Evolution-Licensed Assisted Access (LTE-LAA) with Wi-Fi Coexistence in Unlicensed Spectrum

Long-Term Evaluation-Licensed Assisted Access (LTE-LAA) has good potential for fair coexistence with Wi-Fi in an unlicensed spectrum. Though the LTE-LAA utilizes the same listen before-talk technique as the distributed coordination function in IEEE 802.11, it utilizes completely different parameters and transmission durations. For this reason, a fair coexistence between LTE-LAA and Wi-Fi leaves an open question on how the LTE-LAA network should choose its parameters. To tackle this issue, an analytical framework considering the effects of varying important parameters, which are the different initial back-off window sizes, the numbers of sensing durations, the maximum back-off stages, the number of retransmissions and the transmission opportunities for LTE-LAA and Wi-Fi nodes on their performances has been developed. The node and network airtime performances are evaluated by using the current standard parameters setting to see how this setting affects the node and network airtime performances. From there, optimal settings of the initial backoff window size and number of sensing durations are applied by using the obtained node airtime equation that is derived from the Markov renewal process and evaluated as functions of system parameters. The optimum initial backoff window size and number of sensing durations of LTE-LAA are evaluated and verified by the calculation and simulation using MATLAB software. The analysis shows that LTE-LAA maintained unfair coexistence with Wi-Fi by using the current standard parameter setting as its initial back off window size or sensing duration. But in contrast, using the optimum initial backoff window size and number of sensing durations of LTE-LAA shows that they can maintain proportional fairness. It is unconcealed that the initial backoff window size tuning of LTE-LAA carries a high possibility of achieving fairness because it needs less system data and achieves a higher exactness result.

Pattern Formation in Mesic Savannas

We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations. Homogeneous solutions dominate the dynamics of the standard forest-savanna model, regardless of the length scales of the various spatial processes considered. However, several different pattern-forming scenarios are possible upon including spatial resource limitation, such as competition for water, soil nutrients, or herbivory effects. Using numerical simulations and continuation, we study the nature of the resulting patterns as a function of system parameters and length scales, uncovering subcritical pattern-forming bifurcations and observing significant regions of multistability for realistic parameter regimes. Finally, we discuss our results in the context of extant savanna-forest modeling efforts and highlight ongoing challenges in building a unifying mathematical model for savannas across different rainfall levels.

Transient response of energy harvesting systems with multi-well potential under Poisson white noise excitations

This paper studies the transient response of vibration-based energy harvesting (VEH) systems characterized by multi-well potential functions exposed to Poisson white noise excitations. With the recently developed radial basis function neural networks (RBFNN) approach, the generalized Fokker–Planck–Kolmogorov (GFPK) equation in three-dimensional state space for the transient probability density function (PDF) is solved. The trial solution is composed of a series of radial basis Gaussian functions, each multiplied by a time-varying weight coefficient. The method of Lagrange multiplier is introduced for the constraint of weight coefficients to normalized the trial solution of the PDF solution. As examples to validate the proposed solution approach, the mono-stable and tri-stable energy harvester systems are studied. Monte Carlo simulations (MCS) have been applied to check the analytical solution. Some theoretical trends of the harvested mean square voltage (MSV) as a function of system parameters are examined. The non-Gaussian excitation and time-varying nature of the system can significantly affect the MSV output. It is noted that this work provides researchers and engineers a tool to optimize energy harvesting systems operated in random environment.

Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state solutions of PDEs for multiple combinations of control parameters and initial conditions. Therefore, constructing efficient reduced order models (ROMs) that enable accurate but fast predictions, while retaining the dynamical characteristics of the physical phenomenon as parameters vary, is of paramount importance. In this work, a data-driven, non-intrusive framework which combines ROM construction with reduced dynamics identification, is presented. Starting from a limited amount of full order solutions, the proposed approach leverages autoencoder neural networks with parametric sparse identification of nonlinear dynamics (SINDy) to construct a low-dimensional dynamical model. This model can be queried to efficiently compute full-time solutions at new parameter instances, as well as directly fed to continuation algorithms. These aim at tracking the evolution of periodic steady-state responses as functions of system parameters, avoiding the computation of the transient phase, and allowing to detect instabilities and bifurcations. Featuring an explicit and parametrized modeling of the reduced dynamics, the proposed data-driven framework presents remarkable capabilities to generalize with respect to both time and parameters. Applications to structural mechanics and fluid dynamics problems illustrate the effectiveness and accuracy of the proposed method.

Differentially Private LQ Control

As multi-agent systems proliferate and more user data, new approaches are needed to protect sensitive data while still enabling system operation. To address this need, this article presents a private multiagent LQ control framework. Agents’ state trajectories can be sensitive, and we therefore protect them using differential privacy. We quantify the impact of privacy along three dimensions: the amount of information shared under privacy, the control-theoretic cost of privacy, and the tradeoffs between privacy and performance. These analyses are done in conventional control-theoretic terms, which we use to develop guidelines for calibrating privacy as a function of system parameters. Numerical results indicate that system performance remains within desirable ranges, even under strict privacy requirements.

Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

In this work we propose a \mathbb{Z}_NℤN clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with N^2N2 (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

Discovering Noncritical Organization: Statistical Mechanical, Information Theoretic, and Computational Views of Patterns in One-Dimensional Spin Systems.

We compare and contrast three different, but complementary views of “structure” and “pattern” in spatial processes. For definiteness and analytical clarity, we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well-suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge, thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy—an information theoretic measure of memory—serves to detect ordered, low entropy density patterns. It is superior in several respects to other functions used to probe structure, such as magnetization and structure factors. -Machines—the main objects of computational mechanics—are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities embedded in spin systems—how they store, transmit, and manipulate configurational information to produce spatial structure.

The generation of diverse traveling pulses and its solution scheme in an excitable slow-fast dynamics.

In this article, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modeled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of propagating pulses. The symmetric or asymmetric nature of traveling pulses is characterized, and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions, and show how system parameters and coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves.

Machine learning of phase transitions in nonlinear polariton lattices

Polaritonic lattices offer a unique testbed for studying nonlinear driven-dissipative physics. They show qualitative changes of their steady state as a function of system parameters, which resemble non-equilibrium phase transitions. Unlike their equilibrium counterparts, these transitions cannot be characterised by conventional statistical physics methods. Here, we study a lattice of square-arranged polariton condensates with nearest-neighbour coupling, and simulate the polarisation (pseudospin) dynamics of the polariton lattice, observing regions with distinct steady-state polarisation patterns. We classify these patterns using machine learning methods and determine the boundaries separating different regions. First, we use unsupervised data mining techniques to sketch the boundaries of phase transitions. We then apply learning by confusion, a neural network-based method for learning labels in a dataset, and extract the polaritonic phase diagram. Our work takes a step towards AI-enabled studies of polaritonic systems.

High Resolution MIMO Radar Sensing With Compressive Illuminations

We present a compressive radar design that combines multitone linear frequency modulated (LFM) waveforms in the transmitter with a classical stretch processor and sub-Nyquist sampling in the receiver. The proposed compressive illumination scheme has fewer random elements resulting in reduced storage and complexity for implementation than previously proposed compressive radar designs based on stochastic waveforms. We analyze this illumination scheme for the task of a joint range-angle of arrival estimation in the multi-input and multi-output (MIMO) radar system. We present recovery guarantees for the proposed illumination technique. We show that for a sufficiently large number of modulating tones, the system achieves high-resolution in range and successfully recovers the range and angle-of-arrival of targets in a sparse scene. Furthermore, we present an algorithm that estimates the target range, angle of arrival, and scattering coefficient in the continuum. Finally, we present simulation results to illustrate the recovery performance as a function of system parameters.

Spreading of disturbances in realistic models of transmission grids in dependence on topology, inertia and heterogeneity

The energy transition towards more renewable energy resources (RER) profoundly affects the frequency dynamics and stability of electrical power networks. Here, we investigate systematically the effect of reduced grid inertia, due to an increase in the magnitude of RER, its heterogeneous distribution and the grid topology on the propagation of disturbances in realistic power grid models. These studies are conducted with the DigSILENT PowerFactory software. By changing the power generation at one central bus in each grid at a specific time, we record the resulting frequency transients at all buses. Plotting the time of arrival (ToA) of the disturbance at each bus versus the distance from the disturbance, we analyse its propagation throughout the grid. While the ToAs are found to be distributed, we confirm a tendency that the ToA increases with geodesic distance linearly. Thereby, we can measure an average velocity of propagation by fitting the data with a ballistic equation. This velocity is found to decay with increasing inertia. Characterising each grid by its meshedness coefficient, we find that the distribution of the ToAs depends in more meshed grids less strongly on the grid inertia. In order to take into account the inhomogeneous distribution of inertia, we introduce an effective distance r_{mathrm{eff}}, which is weighted with a factor which strongly depends on local inertia. We find that this effective distance is more strongly correlated with the ToAs, for all grids. This is confirmed quantitatively by obtaining a larger Pearson correlation coefficient between ToA and r_{mathrm{eff}} than with r. Remarkably, a ballistic equation for the ToA with a velocity, as derived from the swing equation, provides a strict lower bound for all effective distances r_{mathrm{eff}} in all power grids. thereby yielding a reliable estimate for the smallest time a disturbance needs to propagate that distance as function of system parameters, in particular inertia. We thereby conclude that in the analysis of contingencies of power grids it may be advisable that system designers and operators use the effective distance r_{mathrm{eff}}, taking into account inhomogeneous distribution of inertia as introduced in Eq. (12), to locate a disturbance. Moreover, our results provide evidence for the importance of the network topology as quantified by the meshedness coefficient beta.

Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries

Abstract This paper investigates the effect of gravity modulation on Rayleigh–Bénard convection using the rigid isothermal boundary conditions. We calculate heat transfer results using the Nusselt and mean Nusselt numbers through the finite-amplitude of convection, which we got from the Ginzburg–Landau equation (GLE). The Ginzburg–Landau equation is derived analytically from the Fredholm solvability condition at third order. The finite amplitude equation (GLE) is a function of system parameters and solved numerically. The gravity modulation considered in terms of steady and sinusoidal parts. The sinusoidal part defines gravity modulation in terms of amplitude and frequency. Our study shows that gravity modulation controls the heat transfer results. The amplitude of modulation enhances heat transfer for low frequencies and diminishes for high frequencies. Further, we found that rigid isothermal boundary conditions are diminishing heat transfer than free and isothermal boundaries. Finally, we concluded that rigid isothermal boundary conditions and gravity modulation controls heat transfer results.

Finite Element Analysis-Aided Optimization of Rectangular Coil Assemblies Applied in Electric Vehicle Inductive Chargers

Energy efficiency and leakage magnetic field (LMF) are two important issues in electric vehicle inductive chargers. In this work, the maximum achievable coil efficiency and the corresponding LMF strength are formulated as functions of system parameters, and figures of merits (FOM) are proposed for assessing the efficiency and LMF performance of the coil assembly pair. The impacts of the coil assemblies’ geometric parameters on both FOMs are examined with the aid of finite element analysis (FEA), and measures to improve the FOMs are suggested based on FEA results. A manual optimization process is conducted on a coil assembly pair. Compared with the initial design, the optimized one results in a higher DC-to-DC efficiency and lower LMF strength while consuming less copper. The performance improvement is verified by FEA results and experimental data measured on an 85 kHz electric vehicle inductive charger prototype. The key measures for coil assembly optimization are summarized.

Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy

In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the N-policy under two information levels, respectively, are investigated. We assume that there is no waiting area in front of the server and an arriving customer is served immediately if the server is idle; otherwise (the server is either busy or on a vacation) it has to leave the system to join a virtual retrial orbit waiting for retrials according to the FCFS rules. After a service completion, if the system is not empty, the server becomes idle, available for serving the next customer, either a new arrival or a retried customer from the virtual retrial orbit; otherwise (if the system is empty), the server starts a vacation. Upon the completion of a vacation, the server is reactivated only if it finds at least N customers in the virtual orbit; otherwise, the server continues another vacation. We study this model at two levels of information, respectively. For each level of information, we obtain both equilibrium and optimal balking strategies of customers, and make corresponding numerical comparisons. Through Particle Swarm Optimization (PSO) algorithm, we explore the impact of parameters on the equilibrium and social optimal thresholds, and obtain the trend in changes, as a function of system parameters, for the optimal social welfare, which provides guiding significance for social planners. Finally, by comparing the social welfare under two information levels, we find that whether the system information should be disclosed to customers depends on how to maintain the growth of social welfare.

Analytic-normal-mode frequencies for N identical particles: The microscopic dynamics underlying the emergence and stability of excitation gaps from BCS to unitarity

The frequencies of the analytic normal modes for N identical particles are studied as a function of system parameters from the weakly interacting BCS regime to the strongly interacting unitary regime. The normal modes were obtained previously from a first-order L=0 group theoretic solution of a three-dimensional Hamiltonian with a general two-body interaction for confined, identical particles. In a precursor to this study, the collective behavior of these normal modes was investigated as a function of N from few-body systems to many-body systems analyzing the contribution of individual particles to the collective macroscopic motions. A specific case, the Hamiltonian for Fermi gases in the unitary regime was studied in more detail. This regime is known to support collective behavior in the form of superfluidity and has previously been successfully described using normal modes. Two phenomena that could sustain the emergence and stability of superfluid behavior were revealed, including the behavior of the normal mode frequencies as N increases. In this paper, I focus on a more detailed analysis of these analytic frequencies, extending my investigation to include Hamiltonians with a range of interparticle interaction strengths from the BCS regime to the unitary regime and analyzing the microscopic dynamics that lead to large gaps at unitarity. The results of the current study suggest that in regimes where higher-order effects are small, normal modes an be used to describe the physics of superfluidity from the weakly interacting BCS regime with the emergence of small excitation gaps to unitarity with its large gaps, and can offer insight into a possible microscopic understanding of the behavior at unitarity. This approach could thus offer an alternative to the two-body pairing models commonly used to describe superfluidity along this transition.

Cavity-QED Quantum Simulator of Dynamical Phases of a Bardeen-Cooper-Schrieffer Superconductor.

We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.